YES
TRS:
 {h(f(x, y)) -> f(f(a(), h(h(y))), x)}
 DP:
  Strict:
   {h#(f(x, y)) -> h#(y),
    h#(f(x, y)) -> h#(h(y))}
  Weak:
  {h(f(x, y)) -> f(f(a(), h(h(y))), x)}
  EDG:
   {(h#(f(x, y)) -> h#(h(y)), h#(f(x, y)) -> h#(h(y)))
    (h#(f(x, y)) -> h#(h(y)), h#(f(x, y)) -> h#(y))
    (h#(f(x, y)) -> h#(y), h#(f(x, y)) -> h#(y))
    (h#(f(x, y)) -> h#(y), h#(f(x, y)) -> h#(h(y)))}
   SCCS:
    Scc:
     {h#(f(x, y)) -> h#(y),
      h#(f(x, y)) -> h#(h(y))}
    SCC:
     Strict:
      {h#(f(x, y)) -> h#(y),
       h#(f(x, y)) -> h#(h(y))}
     Weak:
     {h(f(x, y)) -> f(f(a(), h(h(y))), x)}
     BOUND:
      Bound: match(-raise)-DP-bounded by 2
      Automaton:
       {   h#_2(15) -> 5*
           h#_2(10) -> 5*
            h#_2(9) -> 5*
            h#_2(7) -> 5*
           h#_1(11) -> 5*
           h#_1(10) -> 5*
            h#_1(9) -> 5*
            h#_1(7) -> 5*
           h#_0(10) -> 5*
            h#_0(9) -> 5*
            h#_0(7) -> 5*
            h_2(10) -> 15*
             h_2(9) -> 15*
             h_2(7) -> 15*
            h_1(11) -> 13*
            h_1(10) -> 11*
             h_1(9) -> 11*
             h_1(7) -> 11*
            h_0(10) -> 10*
             h_0(9) -> 10*
             h_0(7) -> 10*
              a_1() -> 12*
              a_0() -> 9*
        f_1(14, 14) -> 13*
        f_1(14, 10) -> 15 | 11
         f_1(14, 9) -> 15 | 11
         f_1(14, 7) -> 15 | 11
        f_1(12, 13) -> 14*
        f_0(10, 10) -> 7*
         f_0(10, 9) -> 7*
         f_0(10, 7) -> 7*
         f_0(9, 10) -> 7*
          f_0(9, 9) -> 7*
          f_0(9, 7) -> 7*
         f_0(7, 10) -> 10 | 7
          f_0(7, 9) -> 10 | 7
          f_0(7, 7) -> 10 | 7}
      Strict:
       {h#(f(x, y)) -> h#(y)}
      EDG:
       {(h#(f(x, y)) -> h#(y), h#(f(x, y)) -> h#(y))}
       SCCS:
        Scc:
         {h#(f(x, y)) -> h#(y)}
        SCC:
         Strict:
          {h#(f(x, y)) -> h#(y)}
         Weak:
         {h(f(x, y)) -> f(f(a(), h(h(y))), x)}
         SPSC:
          Simple Projection:
           pi(h#) = 0
          Strict:
           {}
          Qed